Finite Group Databasebeta

← C2×C4×#66971 #15617848

Subgroups — C2×C4×#66971 #15617848

Order 2816.

2810 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C211yesmaximal, characteristic
2C2×C4×#4343C211yesmaximal, characteristic
3C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
4C4×#66971C2116yesmaximal, direct product factor
5C2×#10622797C211yesmaximal, characteristic, complemented
6C2×#10622402C211yesmaximal, characteristic, complemented
7C2×#10622430C211yesmaximal, characteristic, complemented
8C2×#10622502C211yesmaximal, characteristic, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×C4×#4314C211yesmaximal, characteristic, complemented
11C2×C4×#4325C211yesmaximal, characteristic, complemented
12C2×#10622494C211yesmaximal, characteristic, complemented
13C2×#10622416C211yesmaximal, characteristic
14C2×#10622415C211yesmaximal, characteristic, complemented
15C2×C4×#4313C211yesmaximal, characteristic, complemented
16C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C22×#4325C2211yescharacteristic
26C2×#66971C4116yesdirect product factor
27C2×#66971C2218yes—
28C22×#4314C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C22×#4313C2211yescharacteristic
31C4×#4343—24no—
32C4×#4343C2218yes—
33C4×Q8×D11—24no—
34C4×Q8×D11C2218yescomplemented
35C2×#66946—21no—
36C2×#66946C2211yescharacteristic
37C2×#66945—21no—
38C2×#66945C2211yescharacteristic
39C2×C4⋊C4×D11—21no—
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66940—21no—
42C2×#66940C2211yescharacteristic
43C2×C4×D44—21no—
44C2×C4×D44C2211yescharacteristic
45C2×C42×D11—21no—
46C2×C42×D11—21no—
47C2×C42×D11C2211yescharacteristic
48C2×C4×Dic22—21no—
49C2×C4×Dic22C2211yescharacteristic
50C4×C11×Q16C2218yescomplemented
51C2×C11×#107C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×C4×C8×C11C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66899C2211yescharacteristic
57#10622797C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×#66879C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C4×#4326C2218yescomplemented
64C4×#4325C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69C2×C4×C11⋊C8C2211yescharacteristic
70#10622502C2218yescomplemented
71#10622494C2218yescomplemented
72#10622430C2218yescomplemented
73#10622416C2218yes—
74#10622415C2218yescomplemented
75#10622402C2218yescomplemented
76C4×#4314C2218yescomplemented
77C4×#4313C2218yescomplemented
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C2×#4343—22no—
81C2×#4343—24no—
82C2×#4343C2×C418yes—
83C2×#4343C2314yes—
84C2×Q8×D11—22no—
85C2×Q8×D11—24no—
86C2×Q8×D11C2×C418yescomplemented
87C2×Q8×D11C2314yes—
88C22×D44—21no—
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×C4×D11D411yescharacteristic
96C22×C4×D11D411yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×Dic22—21no—
99C22×Dic22C2311yescharacteristic
100C2×C11×Q16C2×C418yescomplemented
101C2×C11×Q16C2314yes—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C4×Q8×C11—22no—
105C4×Q8×C11—22no—
106C4×Q8×C11C2314yes—
107C4×Q8×C11C2314yes—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C42×C11—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115Q8×Dic11—22no—
116Q8×Dic11—22no—
117Q8×Dic11C2314yes—
118Q8×Dic11C2314yes—
119C2×#4326C2×C418yescomplemented
120C2×#4326C2314yes—
121C2×#4325C2×C418yescomplemented
122C2×#4325C2314yes—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11D411yescharacteristic
139C2×C4×Dic11D411yescharacteristic
140C2×C4×Dic11C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143#66971C2×C4164yesdirect product factor
144C2×#4314C2×C418yescomplemented
145C2×#4314C2314yes—
146C2×#4313—24no—
147C2×#4313C2×C418yescomplemented
148C2×#4313C2314yes—
149C2×#4313C2314yes—
150#66946—28no—
151#66946—22no—
152#66946C2314yes—
153#66945—22no—
154#66945—28no—
155#66945C2314yes—
156C4⋊C4×D11—28no—
157C4⋊C4×D11—22no—
158C4⋊C4×D11C2314yes—
159#66940—28no—
160#66940—22no—
161#66940C2314yes—
162C4×D44—28no—
163C4×D44—22no—
164C4×D44C2314yes—
165C42×D11—28no—
166C42×D11—28no—
167C42×D11D414yes—
168C42×D11C2314yes—
169C4×Dic22—22no—
170C4×Dic22—28no—
171C4×Dic22C2314yes—
172C11×#107C2314yes—
173C11×#103C2314yes—
174C11×#103C2314yes—
175C4×C8×C11C2314yes—
176#66899C2314yes—
177#66899C2314yes—
178#66885C2314yes—
179#66881C2314yes—
180#66880C2314yes—
181#66879C2314yes—
182#66879C2314yes—
183#66874C2314yes—
184#66873C2314yes—
185#66872C2314yes—
186#66871C2314yes—
187C4×C11⋊C8C2314yes—
188C2×C4×#137—111nomaximal, Sylow
189C23×D11—21no—
190C23×D11C2×D411yescharacteristic
191C2×Q8×C11—21no—
192C2×Q8×C11—21no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11C22×C414yes—
196C2×Q8×C11C22×C414yes—
197C2×Q8×C11C2412yes—
198C2×Q8×C11C2412yes—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2411yescharacteristic
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212#4343—216no—
213#4343—28no—
214#4343C22×C4116yes—
215Q8×D11—216no—
216Q8×D11—28no—
217Q8×D11C22×C4116yescomplemented
218C2×D44—28no—
219C2×D44—24no—
220C2×D44—21no—
221C2×D44—22no—
222C2×D44C22×C414yes—
223C2×D44C2412yes—
224C2×C4×D11—28no—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—28no—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—24no—
232C2×C4×D11—42no—
233C2×C4×D11—44no—
234C2×C4×D11—44no—
235C2×C4×D11—44no—
236C2×C4×D11C22×C414yes—
237C2×C4×D11C2×D414yes—
238C2×C4×D11C2×D414yes—
239C2×C4×D11C2×D412yes—
240C2×C4×D11#4114yes—
241C2×C4×D11C2412yes—
242C2×Dic22—28no—
243C2×Dic22—24no—
244C2×Dic22—21no—
245C2×Dic22—22no—
246C2×Dic22C22×C414yes—
247C2×Dic22C2412yes—
248C11×Q16C22×C4116yescomplemented
249C2×C8×C11—22no—
250C2×C8×C11C22×C414yes—
251C2×C8×C11C2412yes—
252C2×C8×C11C2412yes—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4C2412yes—
258C11×C4⋊C4C2412yes—
259C42×C11—24no—
260C42×C11—24no—
261C42×C11C2×D412yes—
262C42×C11C2412yes—
263#4326C22×C4116yescomplemented
264#4325C22×C4116yescomplemented
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268C4⋊Dic11—24no—
269C4⋊Dic11—24no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11C2412yes—
273C4⋊Dic11C2412yes—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277C4×Dic11—24no—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11—24no—
282C4×Dic11C2×D414yes—
283C4×Dic11C2×D412yes—
284C4×Dic11C2×D414yes—
285C4×Dic11C2412yes—
286C2×C11⋊C8—22no—
287C2×C11⋊C8C22×C414yes—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290#4314C22×C4116yescomplemented
291#4313—28no—
292#4313C22×C4116yescomplemented
293C22×#137—111no—
294C2×C4×#41—111no—
295C22×C4×Q8—111no—
296C4×#137—1116no—
297C2×#441—111no—
298C2×#441—111no—
299C2×#440—111no—
300C2×#440—111no—
301C2×C4×Q16—111no—
302C2×C4×Q16D1111yescharacteristic, complemented
303C2×C4×SD16—111no—
304C2×C4×SD16—111no—
305C2×#428—111no—
306C2×#417—111no—
307C2×#419—111no—
308C2×C4×M16—111no—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—24no—
313C22×D11—22no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11C4×D414yes—
317C22×D11C22×D412yes—
318Q8×C11—24no—
319Q8×C11—24no—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11C23×C414yes—
323Q8×C11C23×C414yes—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11#13714yescomplemented
334C2×C4×C11C23×C412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C22×D412yes—
338C2×C4×C11C2×#4112yes—
339C2×C4×C11C2511yescharacteristic
340C2×Dic11—24no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11C4×D414yes—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352D44—216no—
353D44—24no—
354D44—22no—
355D44C23×C414yes—
356C4×D11—216no—
357C4×D11—28no—
358C4×D11—216no—
359C4×D11—44no—
360C4×D11—48no—
361C4×D11—48no—
362C4×D11—48no—
363C4×D11C4×D418yes—
364C4×D11C23×C414yes—
365C4×D11C2×#4114yes—
366Dic22—24no—
367Dic22—22no—
368Dic22—216no—
369Dic22C23×C414yes—
370C8×C11—22no—
371C8×C11C23×C414yes—
372C11⋊C8—22no—
373C11⋊C8C23×C414yes—
374C22×#41—111no—
375C23×Q8—111no—
376C2×#137—118no—
377C2×#137—1116no—
378C22×Q16—111no—
379C22×Q16C2×D1111yescharacteristic
380C22×SD16—111no—
381C22×SD16—111no—
382C22×M16—111no—
383C22×M16—111no—
384C4×#41—118no—
385C4×#41—224no—
386C2×C4×Q8—111no—
387C2×C4×Q8—111no—
388C2×C4×Q8—118no—
389C2×C4×Q8—111no—
390C2×C4×Q8—111no—
391C2×C4×Q8—221no—
392C2×C4×Q8—221no—
393C2×C4×Q8—224no—
394C2×C4×Q8C2×D1111yescharacteristic
395C2×C4×Q8C2×D1111yescharacteristic
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4—221no—
399C2×C4×D4—221no—
400C2×#117—111no—
401C2×#117—221no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—221no—
404C22×C42—111no—
405C22×C42—221no—
406C22×C42—221no—
407#441—118no—
408#441—118no—
409#440—118no—
410#440—118no—
411C4×Q16—118no—
412C4×Q16C2×D1118yescomplemented
413C4×SD16—118no—
414C4×SD16—118no—
415#428—118no—
416C2×#107—111no—
417C2×#107C2×D1111yescharacteristic
418C2×#106—111no—
419C2×#106—111no—
420#419—118no—
421#417—118no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103C2×D1111yescharacteristic
427C2×#103C2×D1111yescharacteristic
428C2×#102—111no—
429C2×#102—111no—
430C4×M16—118no—
431C2×#97—111no—
432C2×#97—111no—
433C2×C4×C8—111no—
434C2×C4×C8C2×D1111yescharacteristic
435C22×C11C2×C4×D412yes—
436C22×C11C2×#13712yes—
437C22×C11#57512yes—
438C22×C11C23×D411yescharacteristic
439C2×D11—28no—
440C2×D11—22no—
441C2×D11—22no—
442C2×D11—24no—
443C2×D11—48no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11C2×C4×D414yes—
447C4×C11—24no—
448C4×C11—24no—
449C4×C11—22no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11C2×C4×D412yes—
453C4×C11C2×#13714yescomplemented
454C4×C11C24×C411yescharacteristic
455C4×C11C22×#4111yescharacteristic
456Dic11—24no—
457Dic11—22no—
458Dic11—22no—
459Dic11—42no—
460Dic11—42no—
461Dic11C2×C4×D414yes—
462C2×#41—118no—
463C2×#41—114no—
464C2×#41—222no—
465C2×#41—224no—
466C22×Q8—118no—
467C22×Q8—114no—
468C22×Q8—111no—
469C22×Q8—221no—
470C22×Q8—222no—
471C22×Q8—224no—
472C22×Q8C22×D1111yescharacteristic
473C22×Q8C22×D1111yescharacteristic
474C22×D4—111no—
475C22×D4—221no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—221no—
480C23×C4—221no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4—221no—
484#137—1164no—
485C2×Q16—118no—
486C2×Q16—114no—
487C2×Q16C4×D1118yescomplemented
488C2×Q16C22×D1114yes—
489C2×SD16—118no—
490C2×SD16—114no—
491C2×SD16—118no—
492C2×SD16—114no—
493C2×M16—118no—
494C2×M16—114no—
495C2×M16—114no—
496C2×M16—224no—
497C22×C8—111no—
498C22×C8—111no—
499C22×C8C22×D1111yescharacteristic
500C22×C8C22×D1111yescharacteristic
501C4×Q8—22no—
502C4×Q8—22no—
503C4×Q8—114no—
504C4×Q8—114no—
505C4×Q8—114no—
506C4×Q8—114no—
507C4×Q8—228no—
508C4×Q8—228no—
509C4×Q8—222no—
510C4×Q8—222no—
511C4×Q8—222no—
512C4×Q8—222no—
513C4×Q8C22×D1114yes—
514C4×Q8C22×D1114yes—
515C4×D4—114no—
516C4×D4—114no—
517C4×D4—228no—
518C4×D4—222no—
519C4×D4—228no—
520C4×D4—222no—
521#117—114no—
522#117—228no—
523#117—222no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—228no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C42—21no—
542C2×C42—21no—
543C2×C42—111no—
544C2×C42—111no—
545C2×C42—111no—
546C2×C42—114no—
547C2×C42—114no—
548C2×C42—228no—
549C2×C42—228no—
550C2×C42—221no—
551C2×C42—221no—
552C2×C42—221no—
553C2×C42—221no—
554C2×C42—221no—
555C2×C42C22×D1111yescharacteristic
556#107—114no—
557#107C22×D1114yes—
558#106—114no—
559#106—114no—
560#103—114no—
561#103—114no—
562#103—114no—
563#103—114no—
564#103C22×D1114yes—
565#103C22×D1114yes—
566#102—114no—
567#102—114no—
568#97—114no—
569#97—114no—
570C4×C8—114no—
571C4×C8C22×D1114yes—
572C2×C11C4×#13714yescomplemented
573C2×C11C22×C4×D411yescharacteristic
574C2×C11C22×#13711yescharacteristic
575C2×C11C2×#57511yescharacteristic
576D11—24no—
577D11—44no—
578C24—111no—
579C24—221no—
580#41—1116no—
581#41—2216no—
582#41—228no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—1116no—
588C2×Q8—114no—
589C2×Q8—112no—
590C2×Q8—224no—
591C2×Q8—228no—
592C2×Q8—2216no—
593C2×Q8—228no—
594C2×Q8—221no—
595C2×Q8—222no—
596C2×Q8C2×C4×D1114yes—
597C2×Q8C2×C4×D1114yes—
598C2×Q8C23×D1112yes—
599C2×Q8C23×D1112yes—
600C2×D4—114no—
601C2×D4—112no—
602C2×D4—224no—
603C2×D4—228no—
604C2×D4—221no—
605C2×D4—222no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—111no—
611C22×C4—114no—
612C22×C4—112no—
613C22×C4—114no—
614C22×C4—112no—
615C22×C4—111no—
616C22×C4—111no—
617C22×C4—114no—
618C22×C4—114no—
619C22×C4—224no—
620C22×C4—228no—
621C22×C4—224no—
622C22×C4—224no—
623C22×C4—228no—
624C22×C4—224no—
625C22×C4—221no—
626C22×C4—224no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—224no—
630C22×C4—442no—
631C22×C4—444no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4D4×D1111yescharacteristic
635C22×C4D4×D1111yescharacteristic
636C22×C4C23×D1111yescharacteristic
637Q16—1116no—
638Q16C2×C4×D11116yescomplemented
639SD16—1116no—
640SD16—1116no—
641M16—1116no—
642M16—228no—
643C2×C8—22no—
644C2×C8—114no—
645C2×C8—112no—
646C2×C8—112no—
647C2×C8—222no—
648C2×C8C2×C4×D1114yes—
649C2×C8C23×D1112yes—
650C2×C8C23×D1112yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—112no—
656C4⋊C4—112no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—221no—
662C4⋊C4—221no—
663C4⋊C4—224no—
664C4⋊C4C23×D1112yes—
665C4⋊C4C23×D1112yes—
666C22⋊C4—224no—
667C22⋊C4—224no—
668C22⋊C4—224no—
669C42—24no—
670C42—24no—
671C42—114no—
672C42—114no—
673C42—112no—
674C42—112no—
675C42—224no—
676C42—224no—
677C42—224no—
678C42—224no—
679C42—224no—
680C42D4×D1112yes—
681C42C23×D1112yes—
682C11C2×C4×#13711yescharacteristic, complemented, Sylow
683C23—114no—
684C23—112no—
685C23—222no—
686C23—222no—
687C23—224no—
688C23—222no—
689C23—442no—
690C23—442no—
691C23C2×D4×D1111yescharacteristic
692Q8—24no—
693Q8—24no—
694Q8—22no—
695Q8—22no—
696Q8—114no—
697Q8—2216no—
698Q8—224no—
699Q8—222no—
700Q8C22×C4×D1114yes—
701Q8C22×C4×D1114yes—
702D4—114no—
703D4—2216no—
704D4—224no—
705D4—222no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—114no—
716C2×C4—112no—
717C2×C4—118no—
718C2×C4—114no—
719C2×C4—114no—
720C2×C4—112no—
721C2×C4—112no—
722C2×C4—2216no—
723C2×C4—2216no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—224no—
727C2×C4—222no—
728C2×C4—228no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—444no—
732C2×C4—448no—
733C2×C4—448no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—448no—
737C2×C4#6697114yesdirect product factor
738C2×C4C22×C4×D1112yes—
739C2×C4C2×D4×D1112yes—
740C2×C4C2×D4×D1112yes—
741C2×C4C2×D4×D1111yescharacteristic
742C2×C4#41×D1112yes—
743C2×C4C24×D1111yescharacteristic
744C8—22no—
745C8—114no—
746C8—222no—
747C8C22×C4×D1114yes—
748C22—114no—
749C22—228no—
750C22—222no—
751C22—222no—
752C22—224no—
753C22—448no—
754C22—442no—
755C22—442no—
756C22C4×D4×D1112yes—
757C22C2×#6697112yes—
758C22#1062329912yes—
759C22C22×D4×D1111yescharacteristic
760C4—24no—
761C4—24no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—114no—
766C4—224no—
767C4—222no—
768C4—222no—
769C4—442no—
770C4—442no—
771C4C4×D4×D1112yes—
772C4C2×#6697114yesdirect product factor
773C4C23×C4×D1111yescharacteristic
774C4C2×#41×D1111yescharacteristic
775C2—224no—
776C2—444no—
777C2C4×#6697114yesdirect product factor
778C2C2×C4×D4×D1111yescharacteristic
779C2C22×#6697111yescharacteristic
780C2C2×#1062329911yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
cosocleC2×C4×C11C25
hypercenterC2×C4×Q16D11
hypocenterC11C2×C4×#137
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C4×Q8×D11C2semidirect
4. C4×#66971C2direct (N × H)
5. C2×#10622797C2semidirect
6. C2×#10622402C2semidirect
7. C2×#10622430C2semidirect
8. C2×#10622502C2semidirect
9. C2×C4×#4326C2semidirect
10. C2×C4×#4314C2semidirect
11. C2×C4×#4325C2semidirect
12. C2×#10622494C2semidirect
14. C2×#10622415C2semidirect
15. C2×C4×#4313C2semidirect
16. C2×C4×C11×Q16C2semidirect
26. C2×#66971C4direct (N × H)
34. C4×Q8×D11C22semidirect
50. C4×C11×Q16C22semidirect
57. #10622797C22semidirect
63. C4×#4326C22semidirect
64. C4×#4325C22semidirect
70. #10622502C22semidirect
71. #10622494C22semidirect
72. #10622430C22semidirect
74. #10622415C22semidirect
75. #10622402C22semidirect
76. C4×#4314C22semidirect
77. C4×#4313C22semidirect
86. C2×Q8×D11C2×C4semidirect
100. C2×C11×Q16C2×C4semidirect
119. C2×#4326C2×C4semidirect
121. C2×#4325C2×C4semidirect
143. #66971C2×C4direct (N × H)
144. C2×#4314C2×C4semidirect
147. C2×#4313C2×C4semidirect
217. Q8×D11C22×C4semidirect
248. C11×Q16C22×C4semidirect
263. #4326C22×C4semidirect
264. #4325C22×C4semidirect
290. #4314C22×C4semidirect
292. #4313C22×C4semidirect
302. C2×C4×Q16D11semidirect
333. C2×C4×C11#137semidirect
412. C4×Q16C2×D11semidirect
453. C4×C11C2×#137semidirect
487. C2×Q16C4×D11semidirect
572. C2×C11C4×#137semidirect
638. Q16C2×C4×D11semidirect
682. C11C2×C4×#137semidirect
737. C2×C4#66971direct (N × H)
772. C4C2×#66971direct (N × H)
777. C2C4×#66971direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669712
C2×C4×#43432
C2×C4×Q8×D112
C4×#669712
C2×#106227972
C2×#106224022
C2×#106224302
C2×#106225022
C2×C4×#43262
C2×C4×#43142
C2×C4×#43252
C2×#106224942
C2×#106224162
C2×#106224152
C2×C4×#43132
C2×C4×C11×Q162
C2×C4×#13711